Problem: Rewrite as a simplified fraction. ${2.96\overline{7} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2967.7777...\\ 100x &= 296.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2671}$ ${x = \dfrac{2671}{900}} \text{or} {2 \dfrac{871}{900}}$